In a typical nuclear reactor, energy is produced from fissionable material located in fuel assemblies or bundles within a reactor core. Depletion of the fissionable material occurs throughout the operational life of a nuclear reactor. Operational and refueling cycles are dependent upon fuel depletion in the reactor core. Reactor core depletion is tracked using lattice depletion estimations.
A lattice represents the spatial distribution of fissionable and non-fissionable materials within a portion of the reactor. Lattice depletion estimations incorporate eigenvalue calculations preformed with defined boundary condition. In an operating reactor, a reactor eigenvalue (kreactor) represents the ratio of neutron production to neutron loss (absorption and leakage) within the reactor. Thus, the reactor eigenvalue is one for a self-sustaining reactor, less than one for a subcritical reactor, and greater than one for a supercritical reactor.
Current industry methods assume a fixed reflective boundary condition and solve an auxiliary equation with some simplification (e.g. homogenization) of the lattice to match the operating reactor eigenvalue. However, use of the fixed boundary condition and simplification of the lattice produces a neutron energy spectrum that does not properly account for the actual lattice heterogeneity and boundary effects. Thus, lattice depletion estimations using these methods result in errors in the calculated depletion within the reactor core. These errors can adversely affect fuel utilization, plant availability, operating margins, and fuel damage probabilities.